Title

Authors

Campus Units

Document Type

Article

Publication Version

Published Version

Publication Date

2011

Journal or Book Title

Rocky Mountain Journal of Mathematics

Volume

41

Issue

5

First Page

1471

Last Page

1482

DOI

10.1216/RMJ-2011-41-5-1471

Abstract

A (left) centralizer for an associative ring R is an additive map satisfying T(xy) = T(x)y for all x, y in R. A (left) Jordan centralizer for an associative ring R is an additive map satisfying T(xy+yx) = T(x)y + T(y)x for all x, y in R. We characterize rings with a Jordan centralizer T. Such rings have a T invariant ideal I, T is a centralizer on R/I, and I is the union of an ascending chain of nilpotent ideals. Our work requires 2-torsion free. This result has applications to (right) centralizers, (two-sided) centralizers, and generalized derivations.